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Metals interacting via short-range antiferromagnetic fluctuations areunstable to sign-changing superconductivity at low temperatures. For thecuprates, this leading instability leads to the well known $d-$wavesuperconducting state. However, there is also a secondary instability to anincommensurate charge density wave, with a predominantly $d-$wave form factor,arising from the same antiferromagnetic fluctuations. Recent experiments in thepseudogap regime of the hole-doped cuprates have found strong evidence for sucha charge density wave order and, in particular, the predicted $d-$wave formfactor. However, the observed wavevector of the charge order differs from theleading instability in Hartree-Fock theory, and is that of a subleadinginstability. In this paper, we examine the feedback of superconductingfluctuations on these different charge-density wave states, and find that overat least a small temperature window, they prefer the experimentally observedwavevector.

Feedback of superconducting fluctuations on charge order in the underdoped cuprates